Very large (cat 5 type) systems can affect the air around it, but the trough setup for Bill isn't going to allow it. I don't see any reason to doubt the NHC's cone (I've looked) for Bill.

Confidence in the NHC track is high,and they have been on track so far.

Ana remnants is the not so confident one. It'll probably bring a lot of rain to Florida, especially if it slows down around there like it may. (Wednesday or so) assuming some odd shenanigans doesn't happen with a new center of circulation. It slowing down/dumping rain is a real possibility.